A block is projected on a rough horizontal surface with velocity $v_0$ at $t=0$. At time $t=t_0$ block stops due to friction. Now consider a reference frame $S$ moving with constant velocity $v_0$ in the direction of block. Work done by the friction on the surface from $t=0$ to $t=t_0$, as observed by reference frame $S$ is $(-km{v}_0^2)$. Find $k$.

Q. A horizontal massive platform is moving with a constant velocity $v_s$. At time $t=0$, a small block of mass $m$ is gently placed on the platform. If the coefficient of friction between the block and the platform is $\mu$ the work done by the force of friction on the block in the fixed ground reference frame (from $t=0$ to a sufficiently long time)is

Q. A rail road car is moving with a constant acceleration of $1$ $m/s^2$. A block of $5$ kg is put on a horizontal rough floor in the car. At time $t=0$, velocity of the car is $5$ m/s. Considering friction is sufficient and block is not slipping on the floor, the work done on the block by friction force (as observed from ground frame) during $t=0$ to $t=2$ sec will be (coefficient of friction is ${\mu }_s$):

Q. A block of mass 1 kg is moving at $t=0$ with speed 2 m/s on rough horizontal surface with coefficient of friction 0.2. A horizontal force F is applied in the same direction of velocity which varies with time as shown in figure(b). Find the speed of block at $t=3s$ $(g=10m/s^2)$

Q. A block of mass $m$ is placed on an inclined plane which is moving with constant velocity $v$ in horizontal direction as shown in figure. Then find out work done in ground frame by the friction in time $t$, if the block is at rest with respect to the inclined plane.

Q. A block of mass $1kg$ starts moving at $t=0$ with speed $2m/s$ on rough horizontal surface with coefficient of friction $0.2$. A horizontal force $F$ is applied in the same direction of velocity which varies with time shown in figure (b). Find the speed of particle at $t=3s$ ($g=10m/s^2)$